10 problems

Song, Wei, Zhang, and Zhao's conjecture. For all $k\ge2$ and even $m\ge4$,

Zhao and Wei's conjecture. For all $k\ge2$ and $m\ge2$,

Mao, Wang, Magnant, and Schiermeyer's conjecture. For $k\ge2$,

Fox, Grinshpun, and Pach's conjecture. For positive integers $k$ and $p$,

Su and Liu's conjecture. $H$ is Ramsey-full if and only if $H$ is Gallai-Ramsey-full.

Conjecture. $H$ is Ramsey-full if and only if $H$ is Gallai-Ramsey-full.

Let $W_{2n}$ denote the wheel graph with an even cycle of length $2n$, let $GR_k(H)$ denote the $k$-color Gallai–Ramsey number of a graph $H$, and let $R_2(W_{2n})$ denote the two-…

Let $F_n$ be the fan graph with $n$ triangles, defined by … so that $F_3$ is the fan with three triangles, and let $gr_k(K_3;F_3)$ denote the $k$-color Gallai-Ramsey number of…

The constructive lower-bound conjecture. The displayed inequality holds for all such $r$, $t$, and hypergraphs $H_1,\dots,H_t$. The preceding constructive theorems provide evidence…

Gallai-Ramsey reduction conjecture. For any graph $H$ with no isolated vertices, we have